Journal for History of Mathematics (한국수학사학회지)

The Korean Society for History of Mathematics (한국수학사학회)
권호 표지
DOI QR코드

DOI QR Code

The Role of Principle of Continuity in the Development of Mathematical Knowledge

수학적 지식의 발달에서 연속성 원리의 역할

  • Received : 2013.09.30
  • Accepted : 2014.02.12
  • Published : 2014.02.28
Download PDF
⟨ Previous Next ⟩

Abstract

When imaginary numbers were first encountered in the 16th century, mathematicians were able to calculate the imaginary numbers the same as they are today. However, it required 200 years to mathematically acknowledge the existence of imaginary numbers. The new mathematical situation that arose with a development in mathematics required a harmony of real numbers and imaginary numbers. As a result, the concept of complex number became clear. A history behind the development of complex numbers involved a process of determining a comprehensive perspective that ties real numbers and imaginary numbers in a single category, complex numbers. This came after a resolution of conflict between real numbers and imaginary numbers. This study identified the new perspective and way of mathematical thinking emerging from resolving the conflicts. Also educational implications of the analysis were discussed.

Keywords

References

  1. E. BRIESKORN and H. KNORRER, Plane Algebraic Curves, Birkhauser, 1986.
  2. J. DIEUDONNE, Mathematics-The Music of Reason, Translated by H. G. DALES, J. C. DALES, NY: Springer, 1992.
  3. D. HILBERT, Uber das Unendliche [On the infinite], Mathematische Annalen 95 (1926). Lecture given in Munster, 4 June 1925. English translation in van Heijenoort, From Frege to Godel: A Source Book in Mathematical Logic, 1879-1931 (1967), 367-392.
  4. Israel KLEINER, Excursions in the History of Mathematics, Boston: Birkhauser, 2012.
  5. P. KITCHER, Explanatory Unification and the Causal Structure of the World, in Scientific Explanation, ed. P. KITCHER and W. SALMON, Minneapolis: University of Minnesota Press, 1989, 410-505.
  6. F. KLEIN, Elementary Mathematics from an Advanced Standpoint: Arithmetic.Algebra.Analysis, NY: Dover Publications, 1968.
  7. G. W. LEIBNIZ, Philosophical Papers and Letters, translated by Leroy E. Loemker, 2nd ed. Dordrecht: D. REIDEL, 1970.
  8. Ernst MACH, The Science of Mechanics: a critical and historical account of its development, Chicago: Open Court, 1919.
  9. A. SIERPINSKA, Understanding in mathematics, Washington, D.C.: Falmer, 1994.
  10. H. STEIN, Logos, Logic, and Logistike: Some Philosophical Remarks on the 19th century Transformation of Mathematics, History and Philosophy of Modern Mathematics, edited by W. ASPRAY & P KITCHER, Minnesota Studies in the Philosophy of Science, vol. XI; University of Minnesota Press, 1988, 238-259.
  11. H. STEINBRING, The Construction of New Mathematical Knowledge in Classroom Interaction, Springer, 2005.
  12. Hermann WEYL, Philosophy of Mathematics and Natural Science, 1960.
  13. Mark WILSON, Frege: The Royal Road from Geometry, Nous 26(2) (1992), 149-180. https://doi.org/10.2307/2215733
  14. Johannes WITT-HANSEN, Leibniz and Contemporary Science, Orbis Litterarum 22(1) (1967), 222-240. https://doi.org/10.1111/j.1600-0730.1967.tb00460.x